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mathematics
applied calculus
Calculus And Its Applications 14th Edition Larry Goldstein, David Lay, David Schneider, Nakhle Asmar - Solutions
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.x-3 · x7
Compute f (1), f (2), and f (3). f(x) = TT.X² 1 + x 4x for x < 2 for 2 ≤ x ≤ 2.5 for 2.5 < x
A store estimates that the total revenue (in dollars) from the sale of x bicycles per year is given by the function R(x) = 250x - .2x2.(a) Graph R(x) in the window [200, 500] by [42000, 75000].(b) What sales level produces a revenue of $63,000?(c) What revenue is received from the sale of 400
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(2x)4
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. .3 -2 y
Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial.f (x) = x3 - 22x2 + 17x + 19
Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial.f (x) = x4 - 200x3 - 100x2
Figure 14(a) shows the number 2 on the x-axis and the graph of a function. Let h represent a positive number and label a possible location for the number 2 + h. Plot the point on the graph whose first coordinate is 2 + h, and label the point with its coordinates. y y = f(x) 2 Figure 14 (a) X
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. X -4 43
Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial.f (x) = 3x3 + 52x2 - 12x - 12
A brokerage firm charges 6% commission on gold purchases in amounts from $50 to $3000. For purchases exceeding $3000, the firm charges 2% of the amount purchased plus a $15 handling fee. Let x denote the amount of gold purchased (in dollars), and let f (x) be the commission charge as a function of
Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial.f (x) = 2x5 - 24x4 - 24x + 2
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(-3x)3
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. T ZA.XA
Figure 14(b) shows the number a on the x-axis and the graph of a function. Let h represent a negative number and label a possible location for the number a + h. Plot the point on the graph whose first coordinate is a + h, and label the point with its coordinates. У (b) y = f(x) a X
When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the formwhere x is the concentration of acetylcholine (in
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 3x²\3 2y
What is wrong with entering the functioninto a graphing utility as Y1 = 1/X + 1? f(x) = 1 x + 1
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. X xºy
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 -5 x
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(9x)-1/2
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x /x
Graph the function with the specified viewing window setting. f(x) = 2 X 1 +1 [-4, 4] by [-.5, 1.5]
What is wrong with entering the function f (x) = x3/4 into a graphing utility as Y1 = X^3/4?
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents X 4x 5/2
Graph the function with the specified viewing window setting.f (x) = -x2 + 2x + 2; [-2, 4] by [-8, 5]
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 x²y
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0. f(x) g(x)
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents (-27x5)2/3 .3 X
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(16x8)-3/4
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(-8y9)2/3
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0. g(x) f(x)
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(-32y-5)3/5
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0. f(x) V g(x)
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.f (x)g(x)
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0. Vf(x)g(x)
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0. Vf(x)g(x)
Find the missing factors. 2x2/3-x-1/3 = x-1/3(
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.[ f (x)]3g(x)
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.[ f (x)g(x)]3
Find the missing factors. √x - - Vx - Vx
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.f (g(x))
Find the missing factors. x-1/4 + 6x1/4 = x-1/4(
Find the missing factors. X y = √xy()
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.g( f (x))
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.f (f(x))
Let f (x) = 3√x and g(x) = 1/x2. Calculate the following functions. Take x > 0.g(g(x))
Find the missing factors.Explain why √a · √b = √ab.
Find the missing factors.Explain why √a/√b = √a/b.
Evaluate f (4).f (x) = x2
Evaluate f (4).f (x) = x3
Evaluate f (4).f (x) = x-1
Evaluate f (4).f (x) = x1/2
Evaluate f (4).f (x) = x3/2
Evaluate f (4).f (x) = x-1/2
Evaluate f (4).f (x) = x-5/2
Evaluate f (4).f (x) = x0
Calculate the compound amount from the given data.principal = $500, compounded annually, 6 years, annual rate = 6%
Calculate the compound amount from the given data.principal = $700, compounded annually, 8 years, annual rate = 8%
Calculate the compound amount from the given data.principal = $50,000, compounded quarterly, 10 years, annual rate = 9.5%
Calculate the compound amount from the given data.principal = $20,000, compounded quarterly, 3 years, annual rate = 12%
Calculate the compound amount from the given data.principal = $100, compounded monthly, 10 years, annual rate = 5%
Calculate the compound amount from the given data.principal = $500, compounded monthly, 1 year, annual rate = 4.5%
Calculate the compound amount from the given data.principal = $1500, compounded daily, 1 year, annual rate = 6%
Calculate the compound amount from the given data.principal = $1500, compounded daily, 3 years, annual rate = 6%
Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the daughter’s 18th birthday?
Assume that a couple invests $4000 each year for 4 years in an investment that earns 8% compounded annually. What will the value of the investment be 8 years after the first amount is invested?
Assume that a $500 investment earns interest compounded quarterly. Express the value of the investment after 1 year as a polynomial in the annual rate of interest r.
Assume that a $1000 investment earns interest compounded semiannually. Express the value of the investment after 2 years as a polynomial in the annual rate of interest r.
Convert the numbers from graphing calculator form to standard form (that is, without E).5E-5
Convert the numbers from graphing calculator form to standard form (that is, without E).8.103E-4
Convert the numbers from graphing calculator form to standard form (that is, without E).1.35E13
Convert the numbers from graphing calculator form to standard form (that is, without E).8.23E-6
The lifetime of a certain computer monitor is an exponential random variable with an expected value of 5 years. The manufacturer sells the monitor for $100, but will give a complete refund if the monitor burns out within 3 years. Then, the revenue that the manufacturer receives on each monitor is a
Let X be a continuous random variable with values between A = 1 and B = ∞, and with the density function f (x) = 4x-5. Compute E(X ) and Var (X ).
What is Pr (X = n) for a geometric random variable with parameter p (the probability of success)? What is E(X ) in this case?
Whenever a document is fed into a high-speed copy machine, there is a .5% chance that a paper jam will stop the machine.(a) What is the expected number of documents that can be copied before a paper jam occurs?(b) Determine the probability that at least 100 documents can be copied before a paper
A needle of length 1 unit is dropped on a floor that is ruled with parallel lines, 1 unit apart. [See Fig. 3.] Let P be the lowest point of the needle, y the distance of P from the ruled line above it, and θ the angle the needle makes with a line parallel to the ruled lines. Show that the needle
Let X be a geometric random variable with parameter p < 1. Find a formula for Pr (X < n), for n > 0. The partial sum of a geometric series with ratio r is given by 1+r+ + pn-] = n 1 - p." 1-r
Find the expected values and the standard deviations (by inspection) of the normal random variables with the density functions given in Exercises. 1 V2T e-(1/2)(x+5)²
Find the expected values and the standard deviations (by inspection) of the normal random variables with the density functions given in Exercises. 1 V2T -(1/2)(x-4)²
The amount of milk (in thousands of gallons) that a dairy sells each week is a random variable X with the density function f (x) = 4(x - 1)3, 1 ≤ x ≤ 2. (See Fig. 4.)(a) What is the likelihood that the dairy will sell more than 1500 gallons?(b) What is the average amount of milk that the dairy
When preparing a bid on a large construction project, a contractor analyzes how long each phase of the construction will take. Suppose that the contractor estimates that the time required for the electrical work will be X hundred worker-hours, where X is a random variable with density function f
A point is selected at random from the rectangle of Fig. 2; call its coordinates (θ, y). Find the probability that y ≤ sin θ. 1 0 Figure 2 77 9
What is Pr (X = n) for a Poisson random variable with parameter λ? What is E(X ) in this case?
How is an integral involving a normal density function converted to an integral involving a standard normal density function?
At a certain junior high school, two-thirds of the students have at least one tooth cavity. A dental survey is made of the students. What is the probability that the first student to have a cavity is the third student examined?
The density function of a continuous random variable X is f (x) = 3x2, 0 ≤ x ≤ 1. Sketch the graph of f (x) and shade in the areas corresponding to (a) Pr (X ≤ .3); (b) Pr (.5 ≤ X ≤ .7);(c) Pr (.8 ≤ X ).
The density function of a continuous random variable X isSketch the graph of f (x) and shade in the areas corresponding to(a) Pr (X ≤ 1); (b) Pr (2 ≤ X ≤ 2.5);(c) Pr (3.5 ≤ X ). f(x) = {x, 0≤x≤ 4. TX,
Consider a group of patients who have been treated for an acute disease such as cancer, and let X be the number of years a person lives after receiving the treatment (the survival time). Under suitable conditions, the density function for X will be f (x) = ke-kx for some constant k.(a) The survival
At a certain bus stop the time between buses is a random variable X with the density function f (x) = 6x(10 - x)/1000, 0 ≤ x ≤ 10. Find the average time between buses.
What is a standard normal random variable? Write the density function.
In a certain town, there are two competing taxicab companies, Red Cab and Blue Cab. The taxis mix with downtown traffic in a random manner. There are three times as many Red taxis as there are Blue taxis. Suppose that you stand on a downtown street corner and count the number X of Red taxis that
Suppose that the average life span of an electronic component is 72 months and that the life spans are exponentially distributed.(a) Find the probability that a component lasts for more than 24 months.(b) The reliability function r (t) gives the probability that a component will last for more than
The annual incomes of the households in a certain community range between 5 and 25 thousand dollars. Let X represent the annual income (in thousands of dollars) of a household chosen at random in this community, and suppose that the probability density function for X is f (x) = kx, 5 ≤ x ≤
The amount of time (in minutes) that a person spends reading the editorial page of the newspaper is a random variable with the density function f (x) = 1/72 x, 0 ≤ x ≤ 12. Find the average time spent reading the editorial page.
What is the density function for a normal random variable with mean μ and standard deviation σ?
The quality-control department at a sewing machine factory has determined that 1 out of 40 machines does not pass inspection. Let X be the number of machines on an assembly line that pass inspection before a machine is found that fails inspection.(a) Write the formula for Pr (X = n).(b) What is the
Find the value of k that makes the given function a probability density function on the specified interval.f (x) = k(3x - x2), 0 ≤ x ≤ 3
In a study of the vacancies occurring in the U.S. Supreme Court, it has been determined that the time elapsed between successive resignations is an exponential random variable with expected value 2 years.Find the probability that the composition of the U.S. Supreme Court will remain unchanged for a
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